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The Perplexing Physics of Imaging a Black Hole

It's a big day for astronomy (and all humans, really). The first image of a black hole has been released. It was created using the Event Horizon Telescope—a collaboration of radio telescopes around the world. This image shows the material around a super massive black hole in the center of a galaxy some 55 million light-years away.

Yes, there is a ton of cool physics here, involving the crazy gravitational things that happen in extreme cases like a black hole. But that's not what I want to look at. Instead, I want to go over some of the more basic physics questions related to this image.

Is it hard to see a black hole because it's black?

No—well, yes. It is true that black holes are black. We normally see things like stars and stuff because the light that they emit travels all the way to our telescopes (or straight into our eyes) and we detect them. Black holes are indeed black. They don't emit visible light (because of crazy gravity stuff) so you can't see them.

But that's not the big problem with a black hole. If we had one in our solar system, you could see it. You could see the warping of space due to its presence and you could see the stuff orbiting the black hole. If you've seen the movie Interstellar, you might have a feeling for what a black hole would look like up close. That visualization of a black hole was created with the help of astrophysicist Kip Thorne.

The black hole is so hard to see because it's tiny. OK, it's not tiny in the sense of an ant. It's tiny in the sense that a human is tiny when viewed from a mile away. To visualize something, we need to consider not just its size but its distance. The better term to use is the angular size. If you turn your head all the way around in a circle, that would be a 360-degree angular view (but don't do that without also turning your body). If you hold your thumb out at arm's length, that is about half a degree of angular size. This is about the same angular size as the moon—which is why you can cover up the moon with your thumb.

So, what about the size of this stuff around the black hole? Yes, it's huge. But it's also about 55 million light-years away. That means it is so far away that light (traveling at 3 x 108 meters per second) would take 55 million years to get there. It's super far. But really, it's the angular size. The black hole (at least the part you can see) would have an angular size of around 40 microarcseconds.

What is a microarsecond? Well, a circle is broken into degrees (for ancient reasons). Each degree can be broken into 60 arcminutes and each minute is 60 arcseconds. Then if you break this arcsecond into a million pieces—you get a microarcsecond. Remember how the moon is 0.5 degrees in angular size (as viewed from the Earth)? That means the angular size of the moon is 45 million times greater than the size of the black hole stuff. The black hole is angular-tiny.

Wait. It gets worse. Because of diffraction, we can't see angular-tiny things. When light passes through an opening (such as a telescope or the pupil of your eye), light diffracts. It bends in a way that interferes with the rest of the light passing through the opening. In the case of the eye (with visible) light, this means that humans can resolve objects with an angular size of about 1 arcminute.

That means that something as angular-tiny (I'm going to keep using that phrase) as a black hole is pretty difficult to resolve to get an image.

How do you overcome the diffraction limit?

Fine. Angular-tiny things are really difficult to see—then how do we see the stuff around a black hole? The angular resolution of a telescope really just depends on two things: the size of the opening and the wavelength of light. Using smaller wavelengths (like ultraviolet or x-rays) gives a better resolution. But in this case the telescope uses a wavelength of light in the millimeter range. This is a pretty large wavelength compared to visible light, which is in the the 500 nanometer range. So, that's bad.

That means the only way to overcome this diffraction limit is to make a bigger telescope. That's exactly what the Event Horizon Telescope does. It essentially makes a telescope the size of the Earth. That's crazy but true. By taking data from multiple radio telescopes in different parts of the world, you can combine the data to make them into one GIANT telescope. It's tricky, but that's what it does. Even with this, there are some problems. With just a handful of telescopes, the EHT group uses some analysis techniques to determine the most probable image from the data collected. But this will allow them to get the image of some super angular-tiny thing—like the stuff around a black hole.

Is this an actual photo of a black hole?

If you look through a telescope and see Jupiter, you are actually seeing Jupiter. Side note: if you haven't done this before, you totally should do it. It's awesome. The light from the sun reflects off the surface of Jupiter and then travels through the telescope and into your eye. Boom. Jupiter. It's real.

That's not what is happening here with this black hole. The image that you see isn't even in the visible range. It's a radio image using wavelengths of light in the radio region. So, what's the difference between radio waves and visible light? Really, it's just the wavelength that's different.

Both light and radio waves are electromagnetic waves. They are a propagation of a changing electric field along with a changing magnetic field (at the same time). These waves travel at the speed of light—because they are light. However, since radio and visible light have different wavelengths, they interact differently with matter. If you turn on your radio inside your house, you can get a signal from a nearby radio station. These radio waves go right through your walls. Visible light, on the other hand, does NOT go through walls.

This also applies to images. If you have visible light from an object, you can see it with your eye and you can record this image on film (yes, that's old school) or with a digital detector (a CCD camera). This image can then be displayed with a computer monitor so that you are pretty much seeing what it actually looks like. This is what happens when you display a visible light image of the moon.

For the stuff around the black hole, it's not a visible light image. It's a radio image. Each pixel on the image you see represents some particular wavelength of a radio wave. When you see the orange parts of the image, that's a false color representation of a wavelength somewhere around 1 millimeter. The same thing happens if you want to "see" an image from infrared or ultraviolet. We have to convert these wavelengths to something we see.

So, that black hole image is not a normal photograph. It's not something you could see if you looked through a telescope—but it's still really awesome.